Stiefel-Whitney Classes for Finite Special Linear Groups of Even Rank

We compute the total Stiefel-Whitney Classes (SWCs) for orthogonal representations of special linear groups SL(n,q) when n and q are odd. These classes are expressed in terms of character values at diagonal elements of order $2$. We give several consequences, and work out the $4$th SWC explicitly, and the $8$th SWC when the $4$th vanishes.